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NCTM Fooled Me Twice, but No More

Apr 26, 2017 by

by Danaher M. Dempsey, Jr. –

Mark Twain : “It’s easier to fool people than to convince them that they have been fooled.”

Looking at the history of the National Council of Teachers of Mathematics (NCTM) activity in pedagogies pushed, textbooks recommended, sorta-standards designed, points of emphasis made, switches of horses in midstream, and results, I say:

“It’s easier to fool the NCTM than to convince them that they have been fooled.”

While these days few persons argue with the push to increase student proficiency in the following:

#1 Procedural Fluency,

#2 Problem Solving, and

#3 Conceptual Understanding,

it remains to be seen if the NCTM can figure out the best ways to do that or even a pretty good way to increase proficiency.  Given NCTM history, it is Buyer Beware with current NCTM advice.

In the late 1950s and 60s the push was “New Math,” which emphasized “Conceptual Understanding” and had little practice with few examples.  [[death to “example-based instruction” could have been the sub-title]] … and it did not work.

The 1970s were a time of recognition of and attempted recovery from “New Math” damage.

The 1980s became a time for  “developing national standards” that culminated in the 1989 NCTM Curriculum and Standards publication.  These were not measurable performance standards but really were recommendations for habits of the mind.  National Science Foundation (NSF) funding made institutions richer as they developed math materials and programs that downplayed practice and pushed new ways of thinking not constrained by the practicing of arithmetic skills, which traditionally had used the four historically-based algorithms of arithmetic and required some memorization.

As this train was running off the rails, John Saxon began selling what many non-NCTM folks saw as a cure for NCTM nonsense: Saxon Math.  It emphasized procedural fluency, with incremental development, constant review of concepts in one-day lessons, frequent testing after five lessons that allowed for immediate reteaching, and avoidance of chapters which he called hunk learning. Half of the 30 problems per day were on procedures and half on story problems.    Saxon’s approach was a huge departure from the “facilitated inquiry” approach to “conceptual understanding”. Saxon had retired from the U.S. Air Force as a decorated bomber pilot. He held three engineering degrees and knew about math use in “the real world”. His mantra was that “Results matter”.    He had stacks of stories about schools with successful results with his “Saxon Math” for students from all “subgroups”. He was not impressed with the lack of results coming from students “in the NCTM-promoted programs” of that time.  He was definitely seen as anti-NCTM man. He was in fact hated by them.

Finally in 2006, the NCTM responded to increasing criticism of the 1989 standards and parent revolts called “math wars” by publishing the NCTM Focal Points. This was “a quest for coherence”.  That pretty much described the previous 20 years: ‘Incoherent”.  Core-Plus, Mathland, TERC-Investigations, (IMP) the Interactive Math Program, (CMP) Connected Math Project, etc. had become models of incoherence.

In 2008, Washington State adopted new math standards with recommended instructional materials in an attempt to restore coherence.  However, beginning in 2009, the federally promoted  Common Core State Standards arrived and eventually replaced Washington State’s Math Standards.

Today it is once again a battle to acquire great materials rather than following  the direction advocated by the historically incoherent establishment.  A profusion of untested ideas,  failed materials, and failed ideology is still being peddled.  Good luck in getting local districts to find and buy the good stuff.  Most of the “leaders” they listen to are aligned with the NCTM version of reality. Those folks ignore the words of W. Edwards Deming (1900-1993 the systems expert who enhanced U.S. production in WWII and improved industrial processes in post-war Japan) : “To improve a system requires the intelligent application of relevant data.” Looking at testing from TIMSS, NAEP, and PISA, is there any chance that the Math Gurus would examine the standards and practices of the high scoring East Asian Five (Singapore, Korea, Japan, Hong-Kong, Taipei) instead of the Common Core Standards for Mathematical Practice?  In truth, you cannot convince the NCTM and its members that they have been fooled.

It is my hope that an agreement will be forged on how best to teach math, and in that vein, I offer these guardedly optimistic statements:

  • Whether understanding or procedure comes first ought to be driven by subject matter and student need — not by educational ideology.
  • Prior learning and knowledge are the greatest determinants of what children can learn, regardless of their physical age.
  • Curricula should be both mathematically coherent and logically sequenced for learning from novice to expert.
  • Two important elements in the development of both procedural and problem solving skills are memorization and practice.
  • “Discovery” should not be conflated with “teaching understanding” as if they are one and the same.
  • Mistakes in educational practices should not be maintained  just because of the time spent making them.
  • Student effort can positively influence achievement.
Danaher Dempsey suffered through the New Math in high school.  He served on the Washington State Board of Education’s Math Advisory Panel, which contributed to the development of the 2008 Washington Math Standards.  He has attempted to teach mathematics efficiently and effectively to students in six western states.
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